COMEDK · Maths · 4. Permutation Combination
Given, 5 line segments of lengths \(2,3,4,5,6\) units. Then, the number of triangles that can be formed by joining these segments is
- A \({ }^{5} C_{3}-3\)
- B \({ }^{5} \mathrm{C}_{3}\)
- C \({ }^{5} C_{3}-1\)
- D \({ }^{5} C_{3}-2\)
Answer & Solution
Correct Answer
(A) \({ }^{5} C_{3}-3\)
Step-by-step Solution
Detailed explanation
To form a triangle, 3 line segments are needed. We can choose 3 line segment from 5 line segments in \({ }^{5} C_{3}\) ways. We know that in a triangle, sum of two sides is always greater than third side. So, line segments of length \((2,3,5),(2,3,6)\) and \((2,4,6)\) do not…
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